Achilles, as portrayed in Homer's Iliad, and Antigone, as portrayed in Sophocles' Antigone, face some similar challenges. One issue both face is having to deal with a king who has authority over them, but whose authority they do not respect (Agamemnon in Achilles' case; Creon in Antigone's case).

Achilles and Antigone also have to deal with the death of a loved one. Patroclus is Achilles' best friend, whereas Polyneices is Antigone's brother.

I'm not sure that code of honour, pursuit of glory, and fate are really comparable in the situations of Antigone and Achilles, though.

For one thing, honour for men and women in ancient Greece was gained in two different realms. For men, honour was gained in the public sphere (good counsel in public and good fighting on the battlefield), whereas a woman's honor was acquired in the home (especially maintaining faithfulness to one's husband). Antigone violates what was expected of women by going outside the home to bury Polyneices. Antigone's presence in the public sphere is one of the things about her behavior that irritates Creon. In some sense, though, I suppose we could say that Antigone becomes like Achilles by going into the public sphere and burying her brother, who had fallen on the battlefield.

Regarding the pursuit of glory, while it is clear that Achilles' return to battle is motivated by the pursuit of glory, Antigone is motivated by divine law as opposed to human law ("Zeus did not announce those laws to me"; line 450 in Ian Johnston's translation). Antigone does acknowledge that she can gain glory by burying her brother (line 502), but I'm not sure glory is her primary motivation.

As for fate, Achilles is quite aware of the fate that awaits him if he remains at Troy (death, but glory) or if he leaves (old age, but no glory). Antigone, however, does not appear concerned with fate. Unlike her father Oedipus, Antigone does not seem to have any prophecy hanging over her head regarding her fate.